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Software VNA and Microwave Network Design and Characterisation Software VNA and Microwave Network Design and Characterisation Zhipeng Wu University of Manchester, UK Software VNA and Microwave Network Design and Characterisation Software VNA and Microwave Network Design and Characterisation Zhipeng Wu University of Manchester, UK Copyright © 2007 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone +44 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxed to (+44) 1243 770620. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 6045 Freemont Blvd, Mississauga, ONT, Canada L5R 4J3 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Anniversary Logo Design: Richard J. Pacifico British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 978-0-470-51215-9 (HB) Typeset in 10/12pt Galliard by Integra Software Services Pvt. Ltd, Pondicherry, India Printed and bound in Great Britain by TJ International, Padstow, Cornwall This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production. To Guoping, William and Richard Contents Foreword xv Preface xvii 1 Introduction to Network Analysis of Microwave Circuits 1 1.1 One-Port Network 2 1.1.1 Total Voltage and Current Analyses 2 1.1.2 Transmission-Reflection Analysis 3 1.1.2.1 Voltage and current 3 1.1.2.2 Reflection coefficient 4 1.1.2.3 Power 5 1.1.2.4 Introduction of a1 and b1 5 1.1.2.5 Z in terms of 7 1.1.3 Smith Chart 7 1.1.3.1 Impedance chart 7 1.1.3.2 Admittance chart 8 1.1.4 Terminated Transmission Line 9 1.2 Two-Port Network 10 1.2.1 Total Quantity Network Parameters 10 1.2.2 Determination of Z, Y and ABCD Parameters 11 1.2.3 Properties of Z, Y and ABCD Parameters 12 1.2.4 Scattering Parameters 12 1.2.5 Determination of S-Parameters 14 1.2.6 Total Voltages and Currents in Terms of a and b Quantities 14 1.2.7 Power in Terms of a and b Quantities 14 1.2.8 Signal Flow Chart 15 viii CONTENTS 1.2.9 Properties of S-Parameters 15 1.2.10 Power Flow in a Terminated Two-Port Network 16 1.3 Conversions Between Z, Y and ABCD and S-Parameters 18 1.4 Single Impedance Two-Port Network 21 1.4.1 S-Parameters for Single Series Impedance 21 1.4.2 S-Parameters for Single Shunt Impedance 21 1.4.3 Two-Port Chart 22 1.4.3.1 Single series impedance network 22 1.4.3.2 Single shunt impedance network 23 1.4.3.3 Scaling property 25 1.4.4 Applications of Two-Port Chart 26 1.4.4.1 Identification of pure resonance 26 1.4.4.2 Q-factor measurements 27 1.4.4.3 Resonance with power-dependent losses 27 1.4.4.4 Impedance or admittance measurement using the two-port chart 28 1.5 S-Parameters of Common One- and Two-Port Networks 28 1.6 Connected Two-Port Networks 28 1.6.1 T-Junction 28 1.6.2 Cascaded Two-Port Networks 30 1.6.3 Two-Port Networks in Series and Parallel Connections 31 1.7 Scattering Matrix of Microwave Circuits Composed of One-Port and Multi-Port Devices 32 1.7.1 S-Parameters of a Multi-Port Device 32 1.7.2 S-Parameters of a Microwave Circuit 33 References 37 2 Introduction to Software VNA 39 2.1 How to Install 40 2.2 The Software VNA 41 2.3 Stimulus Functions 42 2.4 Parameter Functions 43 2.5 Format Functions 44 2.6 Response Functions 45 2.7 Menu Block 48 2.7.1 Cal 48 2.7.2 Display 48 2.7.3 Marker 51 2.7.4 DeltaM 53 2.7.5 Setting 54 2.7.6 Copy 55 CONTENTS ix 2.8 Summary of Unlabelled-Key Functions 55 2.9 Preset 56 2.10 Device Under Test 57 2.10.1 Device 59 2.10.2 Circuit 61 2.11 Circuit Simulator 63 2.11.1 Circuit Menu 63 2.11.2 Device Menu 64 2.11.3 Ports Menu 66 2.11.4 Connection Menu 67 2.12 Circuit Simulation Procedures and Example 67 3 Device Builders and Models 73 3.1 Lossless Transmission Line 74 3.2 One- and Two-Port Standards 76 3.3 Discrete RLC Components: One-Port Impedance Load 78 3.4 Discrete RLC Components: Two-Port Series Impedance 79 3.5 Discrete RLC Components: Two-Port Shunt Admittance 80 3.6 General Transmission Line 81 3.7 Transmission Line Components: Two-Port Serial Transmission Line Stub 82 3.8 Transmission Line Components: Two-Port Parallel Transmission Line Stub 83 3.9 Ideal Two-Port Components: Attenuator/Gain Block 85 3.10 Ideal Two-Port Components: 1:N and N:1 Transformer 86 3.11 Ideal Two-Port Components: Isolator 87 3.12 Ideal Two-Port Components: Gyrator 87 3.13 Ideal Two-Port Components: Circulator 88 3.14 Physical Transmission Lines: Coaxial Line 89 3.15 Physical Transmission Lines: Microstrip Line 90 3.16 Physical Transmission Lines: Stripline 94 3.17 Physical Transmission Lines: Coplanar Waveguide 96 3.18 Physical Transmission Lines: Coplanar Strips 98 3.19 Physical Line Discontinuities: Coaxial Line Discontinuities 101 3.19.1 Step Discontinuity 101 3.19.2 Gap Discontinuity 102 3.19.3 Open-End Discontinuity 103 3.20 Physical Line Discontinuities: Microstrip Line Discontinuities 104 3.20.1 Step Discontinuity 104 x CONTENTS 3.20.2 Gap Discontinuity 107 3.20.3 Bend Discontinuity 109 3.20.4 Slit Discontinuity 110 3.20.5 Open-End Discontinuity 110 3.21 Physical Line Discontinuities: Stripline Discontinuities 111 3.21.1 Step Discontinuity 111 3.21.2 Gap Discontinuity 114 3.21.3 Bend Discontinuity 115 3.21.4 Open-End Discontinuity 116 3.22 General Coupled Lines: Four-Port Coupled Lines 116 3.23 General Coupled Lines: Two-Port Coupled Lines 117 3.24 Physical Coupled Lines: Four-Port Coupled Microstrip Lines 119 3.25 Physical Coupled Lines: Two-Port Coupled Microstrip Lines 122 3.26 Lumped Elements: Inductors 123 3.26.1 Circular Coil 123 3.26.2 Circular Spiral 125 3.26.3 Single Turn Inductor 126 3.27 Lumped Elements: Capacitors 127 3.27.1 Thin Film Capacitor 127 3.27.2 Interdigital Capacitor 129 3.28 Lumped Elements: Resistor 129 3.29 Active Devices 130 3.30 Antennas: Dipole Antenna 130 3.31 Antennas: Resonant Antenna 134 3.32 Antennas: Transmission Between Dipole Antennas 135 3.33 Antennas: Transmission Between Resonant Antennas 136 3.34 User-Defined S-Parameters: One-Port Device 137 3.35 User-Defined S-Parameters: Two-Port Device 138 References 139 4 Design of Microwave Circuits 141 4.1 Impedance Matching 141 4.1.1 Impedance Matching Using a Discrete Element 141 4.1.2 Single Stub Matching 142 4.1.3 Double Stub Matching 143 4.2 Impedance Transformers 145 4.2.1 Quarter-Wave Transformer 145 4.2.2 Chebyshev Multisection Matching Transformer 146 4.2.3 Corporate Feeds 148 CONTENTS xi 4.3 Microwave Resonators 149 4.3.1 One-Port Directly Connected RLC Resonant Circuits 149 4.3.2 Two-Port Directly Connected RLC Resonant Circuits 150 4.3.3 One-Port Coupled Resonators 151 4.3.4 Two-Port Coupled Resonators 152 4.3.5 Transmission Line Resonators 154 4.3.6 Coupled Line Resonators 154 4.4 Power Dividers 155 4.4.1 The 3 dB Wilkinson Power Divider 155 4.4.2 The Wilkinson Power Divider with Unequal Splits 156 4.4.3 Alternative Design of Power Divider with Unequal Splits 157 4.4.4 Cohn’s Cascaded Power Divider 158 4.5 Couplers 159 4.5.1 Two-Stub Branch Line Coupler 159 4.5.2 Coupler with Flat Coupling Response 160 4.5.3 Three-Stub Branch Line Coupler 161 4.5.4 Coupled Line Couplers 162 4.6 Hybrid Rings 163 4.6.1 Hybrid Ring Coupler 163 4.6.2 Rat-Race Hybrid 164 4.6.3 Wideband Rat-Race Hybrid 164 4.6.4 Modified Hybrid Ring 165 4.6.5 Modified Hybrid Ring with Improved Bandwidth 165 4.7 Phase Shifters 166 4.7.1 Transmission Line Phase Shifter 166 4.7.2 LC Phase Shifters 167 4.8 Filters 168 4.8.1 Maximally Flat Response 168 4.8.2 Chebyshev Response 168 = 4.8.3 Maximally Flat Low-Pass Filters with c 1 169 = 4.8.4 Chebyshev Low-Pass Filters with c 1 171 4.8.5 Filter Transformations 172 4.8.6 Step Impedance Low-Pass Filters 173 4.8.7 Bandpass and Bandstop Filters Using /4 Resonators 174 4.8.8
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